Teatcup liners having a barrel with various cross-sectional shapes are known. A barrel with a circular cross-sectional shape is common and have an advantage of a fast and complete milking.
U.S. Pat. No. 6,164,243 discloses a teatcup liner comprising a head end portion, a barrel, and an outlet tube. The barrel has a triangular shape with three corner portions and three side portions extending along the length of the barrel. Each of the side portions is curved or bulged outwardly in a rest state.
FR-953,779 discloses another teatcup comprising a shell and a teatcup liner, both having a triangular cross-section with outwardly curved or bulged side portions in a rest state.
Teatcup liners having a barrel with a triangular cross-sectional shape are advantageous in the sense that they are considered to result in a gentle teat treatment during the milking operation. A disadvantage of such triangular or polygonal teatcup liners is, however, that they do not shut off the vacuum completely, resulting in a slower milking.
WO 2009/042022 discloses a teatcup liner having a barrel with a square cross-section.
EP-958 738 discloses a teatcup liner having a barrel with a wave-shape cross-section.
U.S. Pat. No. 8,113,145 discloses a teatcup liner having a barrel with a round cross-section in its upper part portion and a square cross-section in its lower portion to obtain a uniform seal with minimal irritation in the upper portion of a teat and with reduced pressure applied to the lower portion of a teat. In the barrel square portion, one corner-to-corner dimension is greater than the other corner-to-corner dimension to provide different corner radiuses so that the square barrel portion collapses in a roughly diamond shape.
U.S. Pat. No. 6,776,120 discloses teatcup liners of various thickness and with a barrel where at least one of the wall thickness and rib thickness varies as the barrel and the ribs extend axially.